Energy in Collision

Q. An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, first part of mass $1\text{kg}$ moving with a velocity of $12{\text{ms}}^{-1}$ and $2\text{kg}$ second part moving with a velocity of $8{\text{ms}}^{-1}.$ If the third part moves with $4{\text{ms}}^{-1},$ its mass would be

1. $7\text{kg}$
2. $1\text{kg}$
3. $3\text{kg}$
4. $5\text{kg}$

Q. A block moving horizontally on a smooth surface with a speed of $40\text{m/s}$ splits into two parts with masses in the ratio of $1:2$ If the smaller part moves at $60\text{m/s}$ in the same direction, then the fractional change in kinetic energy is

1. $\frac{1}{8}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. $\frac{2}{3}$

Q. Particle $A$ of mass $m_1$ moving with velocity $(\sqrt{3}\hat{i}+\hat{j})\text{m}{\text{s}}^{-1}$ collides with another partice $B$ of mass $m_2$ which is at rest initially. Let $\overrightarrow{V_1}$ and $\overrightarrow{V_2}$ be the velocities of particles $A$ and $B$ after collision respectively. If $m_1=2m_2$ and after collision $\overrightarrow{V_1}=(\hat{i}+\sqrt{3}\hat{j})\text{m}{\text{s}}^{-1},$ the angle between $\overrightarrow{V_1}$ and $\overrightarrow{V_2}$ is :

1. ${15}^{\circ }$
2. ${60}^{\circ }$
3. $-{45}^{\circ }$
4. ${105}^{\circ }$

Q. A particle of mass $m$ is moving with speed $2v$ and collides with a mass $2\text{m}$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at angle ${45}^{\circ }$ with respect to the original direction.
The speed of each of the moving particle will be

1. $\sqrt{2}v$
2. $\frac{v}{\sqrt{2}}$
3. $\frac{v}{\left(2\sqrt{2}\right)}$
4. $2\sqrt{2}v$

Q. A tennis ball is dropped on a horizontal smooth surface. It bounces back after hitting the surface. The force on the ball during the collision is proportional to the degree of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to scale.

1. 
2. 
3. 
4. 

Q. A ball of mass $m$ is released from $A$ inside a smooth wedge of mass $m$ as shown in the figure. What is the speed of the wedge when the ball reaches point $B$?

1. ${\left(\frac{gR}{3\sqrt{2}}\right)}^{1/2}$
2. $\sqrt{2gR}$
3. ${\left(\frac{5gR}{2\sqrt{R}}\right)}^{1/2}$
4. 0

Q. A railway carriage of mass $8000\text{kg}$ is moving with the speed of $54\text{km/hr}$ and collides with the another stationary carriage of same mass. Find the loss in kinetic energy in this process.

1. $600\text{kJ}$
2. $500\text{kJ}$
3. $350\text{kJ}$
4. $450\text{kJ}$

Q. A body of mass $\left(4m\right)$ is lying in $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $\left(m\right)$ move perpendicular to each other with equal speeds $\left(v\right)$. The total kinetic energy generated due to explosion is

1. $m{v}^2$
2. $\frac{3}{2}m{v}^2$
3. $2m{v}^2$
4. $4m{v}^2$

Q. Two balls $A$ and $B$ of masses $2\text{kg}$ each are moving with speeds $1\text{m/s}$ and $2\text{m/s}$ on a frictionless surface. After colliding, ball $A$ returns back with speed $0.5\text{m/s}$, then the maximum potential energy of deformation is

1. $24\text{J}$
2. $4.5\text{J}$
3. $2.4\text{J}$
4. $45\text{J}$

Q. A particle of mass m, kinetic energy $K$ and linear momentum $p$ collides head on elastically with another particle of mass $2m$ at rest. Match the following (after collision) –

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) momentum of first particle}& \text{(P)}\frac{4}{3}p\\ \text{(B) momentum of second particle}& \text{(Q)}\frac{8K}{9}\\ \text{(C) Kinetic energy of first particle}& \text{(R)}-\frac{p}{3}\\ \text{(D) Kinetic energy of second particle}& \left(S\right)\frac{K}{9}\end{array}$

Which of the following option has the correct combination considering column-I and column-II

1. 
   $D\to R$
2. 
   $A\to P$
3. 
   $B\to P$
4. 
   $C\to Q$

Q. A man of mass $40\text{kg}$ is standing on a platform of mass $60\text{kg}$ kept on a smooth horizontal surface. The man starts moving on the platform with a velocity $20\text{m/s}$ relative to the platform. The recoil velocity of the platform is

Q. In an event of head-on elastic collision between two particles, which of the following statements given below is true?

1. Transfer of energy is maximum and is independent of masses.
2. Transfer of energy between the particles is maximum when their mass ratio is unity.
3. Transfer of energy between the particles is maximum when their mass ratio is less than one.
4. Transfer of energy between the particles is maximum when their mass ratio is greater than one.

Q. A ball of mass $4\text{kg}$ moving with velocity $4\text{m/s}$ collides with another identical ball at rest. The kinetic energy of the balls after collision is $\frac{7}{8}$ times of the original. Find the coefficient of restituton $\left(e\right)$.

1. $1$
2. $0.732$
3. $0.866$
4. $0.239$

Q. A mass 'm' moves with a velocity v and collides in-elastically with another identical mass. After collision the $1^{st}$ mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{nd}$ mass after collision.

1. $\frac{2v}{\sqrt{3}}$
2. $v$
3. $\frac{v}{\sqrt{3}}$
4. $\sqrt{3}v$

Q. A projectile of mass $m$ is fired with a velocity $v$ from point $\text{P}$ at an angle ${45}^{\circ }$. Neglecting air resistance, the magnitude of the change in momentum leaving the point $\text{P}$ and arriving at $\text{Q}$ is,

1. $\sqrt{2}mv$
2. $2mv$
3. $\frac{mv}{2}$
4. $\frac{mv}{\sqrt{2}}$

Q. A moving $\alpha$ particle encounters a stationary unknown nucleus. After collision the two nuclei are scattered in mutually perpendicular directions. If some kinetic energy is lost in collision then unknown nucleus must be

1. A proton
2. A nucleus lighter than $\alpha$ - particle
3. A nucleus heavier than $\alpha$ - particle
4. An $\alpha$ - particle

Q. A $4.0\text{kg}$ mass sliding on a frictionless horizontal surface explodes into two equal parts, one moving with $3.0\text{m/s}$ due north and the other with $5.0\text{m/s}$ due ${30}^{\circ }$ north of east. What is the original speed of the mass?

1. $2.5\text{m/s}$
2. $3.5\text{m/s}$
3. $4.5\text{m/s}$
4. $6.5\text{m/s}$

Q. If the kinetic energy of a body increases by $125$%, the percentage increase in its momentum is,

1. $50$%
2. $62.5$%
3. $250$%
4. $200$%

Q. Change in kinetic energy of a particle is equal to work done on it

1. For conservative force
2. For non conservative force
3. In inertial as well as the non-inertial reference frame
4. All of these

Q. Two balls, each of mass $m$, moving in the same direction with speeds $v$ and $3v$, collide with each other. If the collision is perfectly inelastic, find out the loss in kinetic energy.

1. $\frac{1}{2}m{v}^2$
2. $2m{v}^2$
3. $\frac{3}{2}m{v}^2$
4. $m{v}^2$

Q. Check that the ratio $k{e}^2$ /G $m_e{m}_p$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Q. A gaseous mixture consists of 16g of helium and 16g of oxygen. Then ratio Cp/Cv of mixture is :

1. 1.4
2. 1.54
3. 1.59
4. 1.62

Q. Define :
(i) Angle of projection
(ii) Velocity of projection
(iii) Trajectory

Q. A gaseous mixture consists of $16g$ of helium and $16g$ of oxygen. The ratio $\frac{C_P}{C_V}$ of the mixture is

1. $1.59$
2. $1.62$
3. $1.54$
4. $1.4$

Q. Bullets of mass $40g$ each are fired from a machine gun with a velocity of ${10}^{3}m/s$. If the person firing the bullets experience an average force of $200N$, then the number of bullets fired per minute will be:

1. $300$
2. $600$
3. $150$
4. $75$

Q. The molecules of a given mass of gas have a root mean square velocity of $200m.s^{-1}$ at ${27}^{0}C$ and $1.0\times {10}^{5}N.m^{-2}$ pressure. When the temperature is ${127}^{0}C$ and the pressure $0.5\times {10}^{5}N{m}^{-2}$, the root mean square velocity is $m{s}^{-1}$, is

1. $\frac{400}{\sqrt{3}}$
2. $\frac{100\sqrt{2}}{3}$
3. $\frac{100}{3}$
4. $100\sqrt{2}$

Q. When the mass of a body is increased by 100% and velocity of a body is decreased by 50%. What is the percentage change in its kinetic energy?

Q. A particle of mass m, kinetic energy $K$ and linear momentum $p$ collides head on elastically with another particle of mass $2m$ at rest. Match the following (after collision) –

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) momentum of first particle}& \text{(P)}\frac{4}{3}p\\ \text{(B) momentum of second particle}& \text{(Q)}\frac{8K}{9}\\ \text{(C) Kinetic energy of first particle}& \text{(R)}-\frac{p}{3}\\ \text{(D) Kinetic energy of second particle}& \left(S\right)\frac{K}{9}\end{array}$

Which of the following option has the correct combination considering column-I and column-II

1. 
   $C\to S$
2. 
   $D\to P,R$
3. 
   $B\to Q$
4. 
   $A\to P,Q$

Q. A rocket with a lift-off mass $3.5\times {10}^{4}kg$ is blasted upwards with an initial acceleration of $10m/s^2$. The initial thrust of the blast is:

1. $3.5\times {10}^{5}N$
2. $7.0\times {10}^{5}N$
3. $1.40\times {10}^{5}N$
4. $1.75\times {10}^{5}N$

Q. Three closed vessels A, B, and C are at the same temperature T and contain gases which obey the Maxwell distribution of speed. Vessel A contains only $O_2$, B only $N_2$ and C a mixture of equal quantities of $O_2$ and $N_2$. If the average speed of $O_2$ molecules in vessel A is $V_1$, that of the $N_2$ molecules in vessel is $V_2$ then the average speed of the $O_2$ molecules in vessel C will be

1. $(V_1+V_2)/2$
2. $V_1$
3. $(V_1{V}_2{)}^{1/2}$
4. $\frac{V_1}{2}$